142 lines
4.8 KiB
TeX
142 lines
4.8 KiB
TeX
\documentclass[addpoints,11pt]{exam}
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\usepackage{url}
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\usepackage{color}
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\usepackage{hyperref}
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\pagestyle{headandfoot}
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\runningheadrule
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\firstpageheadrule
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\firstpageheader{Scientific Computing}{Project Assignment}{11/02/2014
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-- 11/05/2014}
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%\runningheader{Homework 01}{Page \thepage\ of \numpages}{23. October 2014}
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\firstpagefooter{}{}{{\bf Supervisor:} Jan Benda}
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\runningfooter{}{}{}
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\pointsinmargin
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\bracketedpoints
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%\printanswers
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%\shadedsolutions
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%%%%% listings %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\usepackage{listings}
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\lstset{
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basicstyle=\ttfamily,
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numbers=left,
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showstringspaces=false,
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language=Matlab,
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breaklines=true,
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breakautoindent=true,
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columns=flexible,
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frame=single,
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% captionpos=t,
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xleftmargin=2em,
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xrightmargin=1em,
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% aboveskip=11pt,
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%title=\lstname,
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% title={\protect\filename@parse{\lstname}\protect\filename@base.\protect\filename@ext}
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}
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\begin{document}
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%%%%%%%%%%%%%%%%%%%%% Submission instructions %%%%%%%%%%%%%%%%%%%%%%%%%
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\sffamily
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% \begin{flushright}
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% \gradetable[h][questions]
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% \end{flushright}
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\begin{center}
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\input{../disclaimer.tex}
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\end{center}
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%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{questions}
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\question An important property of sensory systems is their ability
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to discriminate similar stimuli. For example, to discriminate two
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colors, light intensities, pitch of two tones, sound intensity, etc.
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Here we look at the level of a single neuron. What does it mean that
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two similar stimuli can be discriminated given the spike train
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responses that have been evoked by the two stimuli?
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You are recording the activity of a neuron in response to two
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different stimuli $I_1$ and $I_2$ (think of them, for example, of
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two light intensities with different intensities $I_1$ and $I_2$ and
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the activity of a ganglion cell in the retina). The neuron responds
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to a stimulus with a number of spikes. You (an upstream neuron) can
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count the number of spikes of this response within an observation
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time of duration $T$. For perfect discrimination, the number of
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spikes evoked by the stronger stimulus within $T$ is larger than for
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the smaller stimulus. The situation is more complicated, because the
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number of spikes evoked by one stimulus is not fixed but varies.
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How well can an upstream neuron discriminate the two
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stimuli based on the spike counts $n$? How does this depend on the
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duration $T$ of the observation time?
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The neuron is implemented in the file \texttt{lifspikes.m}.
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Call it like this:
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\begin{lstlisting}
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trials = 10;
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tmax = 50.0;
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input = 15.0;
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spikes = lifspikes(trials, input, tmax);
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\end{lstlisting}
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The returned \texttt{spikes} is a cell array with \texttt{trials}
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elements, each being a vector of spike times (in seconds) computed
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for a duration of \texttt{tmax} seconds. The intensity of the stimulus
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is given by \texttt{input}.
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Think of calling the \texttt{lifspikes()} function as a
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simple way of doing an electrophysiological experiment. You are
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presenting a stimulus with an intensity $I$ that you set. The
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neuron responds to this stimulus, and you record this
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response. After detecting the time points of the spikes in your
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recordings you get what the \texttt{lifspikes()} function
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returns.
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For the two inputs $I_1$ and $I_2$ use
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\begin{lstlisting}
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input = 14.0; % I_1
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input = 15.0; % I_2
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\end{lstlisting}
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\begin{parts}
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\part
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Show two raster plots for the responses to the two different
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stimuli. Find an appropriate time window and an appropriate
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number of trials for the spike raster.
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Just by looking at the raster plots, can you discriminate the two
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stimuli? That is, do you see differences between the two
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responses?
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\part Generate properly normalized histograms of the spike counts
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within $T$ (use $T=100$\,ms) of the responses to the two different
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stimuli. Do the two histograms overlap? What does this mean for
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the discriminability of the two stimuli?
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How do the histograms depend on the observation time $T$ (use
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values of 10\,ms, 100\,ms, 300\,ms and 1\,s)?
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\part Think about a measure based on the spike-count histograms
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that quantifies how well the two stimuli can be distinguished
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based on the spike counts. Plot the dependence of this measure as
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a function of the observation time $T$.
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For which observation times can the two stimuli perfectly
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discriminated?
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\underline{Hint:} A possible readout is to set a threshold
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$n_{thresh}$ for the observed spike count. Any response smaller
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than the threshold assumes that the stimulus was $I_1$, any
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response larger than the threshold assumes that the stimulus was
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$I_2$. For a given $T$ find the threshold $n_{thresh}$ that
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results in the best discrimination performance. How can you
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quantify ``best discrimination'' performance?
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\end{parts}
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\end{questions}
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\end{document}
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